Open and exploratory learning ap

Open and exploratory learning approach

There are different perspectives and methods regarding the study of subjects like mathematics and other STEM fields.

Common educational beliefs suggest that learning mathematics requires a strong grasp of current knowledge before moving on to the next level. The rationale behind this is that mathematics is a logical and hierarchical science, where each concept builds upon the previous ones. If the foundation is not solid, it can hinder understanding and application in later stages. This method entails gradually learning new content based on prior knowledge, which helps ensure a solid understanding of the fundamental concepts and skills in mathematics.

However, if there is no pressure for exams and the study of mathematics is approached as an interest or for knowledge enhancement, a more open and exploratory learning approach should be adopted. In this case, the learning of mathematics can involve continuously exploring new content until encountering areas of non-comprehension, then revisiting and reviewing previously overlooked knowledge points. Mathematics is a discipline that requires constant exploration, innovation, and discovery. Each concept has its background and significance, and simply memorizing without understanding can detract from the beauty of mathematics. Moreover, continuous learning of new content through this approach stimulates students' curiosity and interest, allowing them to independently explore different domains of mathematics.

Firstly, striving to completely master current knowledge before learning new concepts is unrealistic. It is difficult to determine when knowledge is "firmly grasped," which can lead to slow progress and repetitive review, resulting in feelings of boredom. Additionally, the process of learning new knowledge can deepen the understanding of current knowledge.

However, if students solely focus on learning new concepts without reviewing and revisiting past material, problems may arise. Mathematical knowledge is cumulative, with new concepts often building upon previous ones. If previous knowledge is not well understood, comprehending new concepts becomes challenging and may lead to "gaps" in understanding. How can this situation be avoided?

This depends on both the students themselves and educational beliefs:

If students are primarily interested in achieving high scores in exams, or if they are under exam pressure or lack significant interest in mathematics, the first method is more reliable. It involves establishing a solid foundation and gradually delving deeper.

If students genuinely enjoy mathematics and aspire to delve deeper or have a better grasp of the knowledge system, while also possessing strong self-study abilities, the second method may be more suitable. It involves expanding their horizons first and then circling back to consolidate their understanding.

Of course, regardless of the chosen method, students need to invest sufficient time and effort, while maintaining their enthusiasm for mathematics.

According to the educational concepts of the information age, we should focus more on cultivating students' enthusiasm for learning, creative thinking, and exploratory abilities. It is far more important for students to grasp the knowledge system of a subject than to be able to solve individual challenging problems. The traditional, step-by-step learning approach often makes it difficult for students to fully grasp the knowledge system they are learning.

Grasping the knowledge system of a subject means having a comprehensive understanding and mastery of its core concepts, principles, methods, and applications. It encompasses the foundational knowledge and key concepts of the subject and demonstrates the relationships and organizational structure among them.

The knowledge system helps students build a foundational understanding of the subject. It provides the core concepts and principles of the subject, helping students understand the basic framework and underlying logic of the subject. The knowledge system showcases the relationships and organizational structure between different concepts and topics in the subject. It helps students understand the connections between various knowledge points, forming a systematic perspective and way of thinking. By mastering the knowledge system, students can delve deeper into the different aspects of the subject. It provides more details and background knowledge, enabling learners to think and apply the knowledge in a more comprehensive manner. The knowledge system serves as the foundation for further learning and development. By establishing a solid knowledge system, students can better explore the frontiers of the subject and expand their understanding and application abilities.

Adopting open and exploratory learning methods can maintain students' enthusiasm and motivation for learning. Continuous acquisition of new knowledge can stimulate interest and maintain learning motivation. Focusing too much on reviewing old knowledge too early can be dull and affect students' interest in learning. At the same time, open and exploratory learning methods also contribute to the establishment of the knowledge system. In the process of learning new knowledge, students can see the connections between different knowledge, which helps them form a systematic knowledge structure rather than isolated knowledge points. This learning method constantly stimulates problem awareness in practice. When encountering new knowledge or concepts, or when facing doubts or difficulties in learning, it sparks problem awareness and drives further exploration and understanding. This learning method is also more efficient as it targets specific areas for review based on students' needs. It is easy to identify the knowledge points that require review and enhanced understanding. This review effect helps consolidate key knowledge in a targeted manner.

Open and exploratory learning methods also pose higher requirements for educators. For example, it requires creating diverse learning experiences by using different learning resources, teaching methods, and learning activities to allow students to engage with and review previous knowledge in different ways. For example, using examples, charts, games, and interactive activities to stimulate students' interest and engagement. Challenging problems and tasks should be provided to students, requiring them to apply previously learned knowledge to solve them. This allows students to consolidate and review old knowledge while developing their problem-solving skills. Guiding students to discover the connections between knowledge is necessary. Helping students recognize the connections and associations between newly learned knowledge and previously acquired knowledge. By demonstrating the continuity of knowledge and the extension of application areas, it can stimulate students' interest in learning and their understanding of the importance of review. Flexibility in adjusting the pace of learning is needed. Based on students' progress and understanding, the learning pace and content can be adjusted flexibly, ensuring that they do not become overly bored or lost during the learning process. When students encounter problems during their learning and lack the ability to resolve them on their own, it is important to identify the knowledge points they most need to review and provide appropriate assistance.

To be precise, open and exploratory learning methods are more suitable for self-learning and higher education stages. This learning method emphasizes the active involvement of learners in the learning process, allowing them to construct knowledge and understanding through independent exploration and discovery.

Self-learning usually requires students to have certain learning abilities and self-management skills, enabling them to autonomously plan their learning progress and choose suitable learning resources. Open and exploratory learning methods provide more flexible and diverse learning paths for self-learning. Students can freely choose the content and approach of their learning, engaging in in-depth exploration based on their interests and learning needs.

In higher education and beyond, open and exploratory learning methods are also more common and popular. Higher education focuses on cultivating students' independent thinking and critical thinking skills, encouraging them to actively engage in knowledge creation and application. Open and exploratory learning methods can help students develop these abilities, fostering their self-directed learning and problem-solving skills.

However, open and exploratory learning methods do not imply completely abandoning guidance and structured learning. In the early stages of learning, especially if this learning method is adopted before higher education, moderate guidance and structure are still necessary, particularly in terms of mastering foundational knowledge and developing skills. But as learners grow and delve deeper into a discipline, open and exploratory learning methods can help them better develop their academic interests and independent thinking abilities.